Chelsea beat Brenford 4-0 thanks to goals from Mata, Oscar, Lampard and Terry. City won by the same score against Leeds.
London: Chelsea broke Brentford's resistance with a potent second-half attacking display to eliminate the third-tier club from the FA Cup at the second attempt with a 4-0 victory on Sunday, while Manchester City won by the same score against Leeds.
Held by Brentford three weeks ago, Chelsea couldn't find a breakthrough until the 54th minute of the fourth-round replay when Juan Mata struck from the edge of the penalty area.
Oscar found the net for the second time in four days, Frank Lampard side-footed in his 199th goal for the club, and captain John Terry completed the 4-0 thrashing with a header.
"They made it very difficult," Terry said. "(They had) two banks of four and sat very deep."
Chelsea will play at Middlesbrough on Feb. 27 in the fifth round. Man City are already through to the quarterfinals after beating second-tier club Leeds.
Yaya Toure put the Premier League champions ahead after five minutes before Sergio Aguero scored from the penalty spot, helped to set up Carlos Tevez's close-range goal after the break and then collected his second off the post.
"It was important we bounced back," City midfielder James Milner said. "They've knocked a few Premier League teams out of cups this season, so it was important we did a job and we did it well. We had to improve on last week, we did that."
In Sunday's late cup match, Wigan were at Huddersfield, while Liverpool played Swansea in the only Premier League fixture of the weekend.
The only cup shocks of the weekend came on Saturday with second-tier club Blackburn winning at Arsenal and third-tier team Oldham drawing with Everton.
Just how lucrative a cup run can be to lower-league teams was highlighted by Brentford estimating that they have earned more than $1 million from the two fourth-round matches against Chelsea.
The seventh-place team in League One - a point behind the playoff places - managed to repel waves of attacks by Chelsea with a disciplined display in the first half.
The visitors even found the net just before half time through Marcello Trotta, but the referee had already blown for a foul on Brentford midfielder Adam Forshaw.
Chelsea's finishing was wayward in the first half, although Oscar did hit the post.
"They were working very, very hard in the first half," Chelsea manager Rafa Benitez said. "To keep this intensity in the second half against a team like Chelsea would be very difficult for them."
And, after the break the intensity was ramped up by Chelsea, with the breakthrough coming after nine minutes.
Goalkeeper Petr Cech launched the ball forward, Demba Ba held off the Brentford defense, and Mata picked up possession before crisply striking into the net. The second was even slicker from Oscar in the 68th.
Eden Hazard, who had just replaced Victor Moses, seized possession near the halfway line and powered into the penalty area where he sent the ball to Branislav Ivanovic. The right back cut the ball back to Oscar, who flicked it into the net through three defenders.
After the struggle scoring in the first half, Chelsea took just three further minutes to make it 3-0. Mata broke down the left flank and squared the ball for an unmarked Lampard to volley into the net.
The 34-year-old midfielder's 199th goal puts him three behind Bobby Tambling's club record, however he hasn't been offered a new contract beyond the end of the season - much to the annoyance of Chelsea fans.
Another member of Chelsea's old guard found the net in the 82nd, with Terry meeting Oscar's cross with a header.
The goal was enthusiastically celebrated by the 32-year-old Terry, whose place in the team has been uncertain since his knee injury.
At Etihad Stadium, a City win seemed certain from the fifth minute after neat link-up play between David Silva, Tevez and Yaya Toure led to the latter rounding goalkeeper Jamie Ashdown and scoring.
Ten minutes later, Aguero was on target from the spot after the Argentina striker had tangled with Tom Lees.
Aguero provided the cross seven minutes after the break that Tevez tapped in at the far post. And Aguero found the net again in the 74th after latching onto Silva's high, defense-splitting pass, and curling past Ashdown off the post.